非负二元函数最大值求解的复变函数法  

COMPLEX METHOD OF SEEKING THE MAXIMUM OF NON-NEGATIVE FUNCTION OF TWO VARIABLES

作　　者：张静[1] 史文谱[2,3] 

机构地区：[1]烟台汽车工程职业学院机电工程系,烟台265500 [2]烟台大学机电汽车工程学院,烟台264005 [3]山东省高校先进制造与控制技术重点实验室,264005

出　　处：《机械强度》2018年第1期111-116,共6页Journal of Mechanical Strength

基　　金：山东省科技攻关项目(2012G0030011)资助~~

摘　　要：二元函数优化问题在许多工程问题中广泛存在,其全局寻优方法一直是人们研究的热点问题之一。基于复变函数中解析函数最大模理论针对一类非负二元函数的全局寻优问题提出了一种高效方法,它可以将目标函数在有界二维区域上的寻优问题简化为一维全局优化问题的求解,给出了方法可行性的理论依据,并用三个算例验证了方法的有效性。方法和结论一方面可直接用于解决解析函数应用场合中的优化问题;另一方面对于适用的二维数学优化问题可实现高精度、高效率的全局寻优。The optimization problems of binary functions widely exist in many practical engineering problems,their global optimization methods have always been one of the hot research issues. A high effective method of global optimization to nonnegative binary functions was put forward basing on the maximum modulus theorem of the analytic function of complex function,this method can simplify the optimization problem of the object function on a two-dimension bounded area as an one-dimension global optimization problem,the theory basis for the optimization method was given,and three numerical examples were given to show the effectiveness of the method. On one hand,the conclusions obtained in this paper can be directly used to solve the optimization problem in which the analytic function theory could be used,on the other hand,it can be used to obtain the global optimization solutions of the two-dimension mathematical optimization problems in which the method could be used in a high precision and high effective manner.

关 键 词：非负二元函数优化 最大值 复变函数法 一维优化 

分 类 号：O221.2[理学—运筹学与控制论]